Yang-Mills theory and the ABC conjecture
We establish a precise correspondence between the ABC Conjecture and N=4𝒩=4<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mi mathvariant="cal">𝒩</mi><mo class="MathClass-rel">=</mo><mn>4</mn>...
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
3 May 2018
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| In: |
International journal of modern physics. A, Particles and fields, gravitation, cosmology
Year: 2018, Jahrgang: 33, Heft: 13 |
| ISSN: | 1793-656X |
| DOI: | 10.1142/S0217751X18500537 |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1142/S0217751X18500537 Verlag: https://www.worldscientific.com/doi/abs/10.1142/S0217751X18500537 
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| Verfasserangaben: | Yang-Hui He, Zhi Hu, Malte Probst and James Read |
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| 520 | |a We establish a precise correspondence between the ABC Conjecture and N=4=4<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mi mathvariant="cal"></mi><mo class="MathClass-rel">=</mo><mn>4</mn></math> super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies’ method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d’enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of N=4=4<math display="inline" overflow="scroll" altimg="eq-00002.gif"><mi mathvariant="cal"></mi><mo class="MathClass-rel">=</mo><mn>4</mn></math> SYM. | ||
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